An optical flow is an apparent velocity distribution on an image, which is generated by relative motion between an observer and an object. Usually the optical flow is expressed as an apparent velocity vector at each point on the image.
In a conventional gradient method, it is assumed that image intensity of the object is conserved after movement in time-varying image processing, and the optical flow is estimated based on a partial differential equation of an equation (1) called an optical flow equation that expresses a conservation law of the image intensity of the object (see Non Patent Document 1). Where I(x,y,t) is the intensity, (x,y) is a coordinate on the image, t is a time, and [u v]T is the optical flow.
Only the equation (1) is not enough for an equation that determines two variables u and v, the equation lacking a constraint condition. Therefore, assuming that all the optical flows are equal to one another in a neighborhood of a particular point, a linear equation of an equation (2) for the optical flow is obtained (see Non Patent Document 5). Where a suffix expresses partial differential like Itx=(∂2/∂t∂x)I. The linear equation gives a fundamental estimation principal of the optical flow. At this point, a Hessian matrix (3) of the intensity is a quantity that is closely related to a corner of the object in the image, and the quantity det(H) related to numerical solvability of the linear equation is also utilized as a degree of reliability of the estimated optical flow.
                              [                      Formula            ⁢                                                  ⁢            1                    ]                ⁢                                                                                                            ⅆ            I                                ⅆ            t                          =                                                                              ∂                  I                                                  ∂                  x                                            ⁢              u                        +                                                            ∂                  I                                                  ∂                  y                                            ⁢              v                        +                                          ∂                I                                            ∂                t                                              =          0                                    (        1        )                                          [                                                                      I                  tx                                                                                                      I                  ty                                                              ]                =                  -                                    [                                                                                          I                      xx                                                                                                  I                      xy                                                                                                                                  I                      xy                                                                                                  I                      yy                                                                                  ]                        ⁡                          [                                                                    u                                                                                        v                                                              ]                                                          (        2        )                                H        =                  [                                                                      I                  xx                                                                              I                  xy                                                                                                      I                  xy                                                                              I                  yy                                                              ]                                    (        3        )            